Okay, wow you are so wrong this will take a while. I'm going to be fully quoting things so as to not deal with partial quote, and out-of-context stuff.
First, from the Character Level glossary entry:
A character's total level. For a character with levels in only one class, class level and character level are the same thing.
Second, from the Class Level glossary entry:
A character's level in a single class. Class features generally depend on class level rather than character level.
Third, from the Hit Die/Dice (HD) glossary entry:
In the singular form, a die rolled to generate hit points. In the plural form, a measure of relative power that is synonymous with character level for the sake of spells, magic items, and magical effects that affect a certain number of Hit Dice of creatures.
In addition, in the DMG under Monstrous Characters (also found on the SRD), it states that to determine total Effective Character Level, you add in any Level Adjustment the creature has, plus it's racial hit dice, plus it's levels in character classes.
Now, to the topic of Bloodlines, and how they interact with the above.
Bloodline levels:
Over the course of his career, a character with a bloodline becomes more powerful than one without a bloodline. Because the power gain is gradual over a span of twenty levels, a static level adjustment doesn't truly reflect this difference. instead, a bloodline character must take one or more levels of "bloodline" at various points in his career, as noted on Table: Bloodline Levels.
Wait, does that actually say "class levels of bloodline"? *checks SRD and UA again* Yup. It certainly says "class levels of bloodline".
So how does this interact? Easily, as shown in the next paragraph of that same entry:
Before a character with a bloodline reaches the indicated character level, he must take one class level of "bloodline." Class levels of "bloodline" do not increase a character's character level the way a normal class level does, but they do provide certain benefits (see below).
Okay, so he must take a bloodline level before he gains the listed character level, or he takes a penalty, stops advancing bloodline abilities, etc. But what is this about "do not increase a character's character level the way a normal class level does" business? Well it says at the end of that same sentence that you should see below. So let's look below:
A bloodline level grants no increase in base attack bonus or base save bonuses, no hit points or skill points, and no class features. It counts as a normal class level (with no class skills) for the purpose of determining maximum skill ranks. Levels of bloodline never result in XP penalties for multiclass characters.
Okay, so no hit points, no skill points, no class features, no bab or saves. It DOES count for skill caps. It never factors in for XP penalties. That's pretty straight forward, right? What about this next part:
Okay. For things that use CLASS LEVEL, include the bloodline level(s) the character has. So arcane caster level, divine spellcaster level, manifester level for psionic character, initiator level, binding level, stunning fist DCs, etc.
In fact, in the next two paragraphs it provides two examples of both.
So, in the end, here is what we have:
-A character takes CLASS LEVELS in bloodline (x), where X is their particular bloodline, such as Celestial Major, or Djinni Minor.
-A bloodline level does not grant base attack bonus or base save bonuses, no hit points or skill points, and no class features.
-A bloodline level counts as a class level for any calculation that uses class level, but not to get additional class features. So a wizard 5/bloodline 2 casts spells at caster level 7, but only has the spells per day of a Wizard 5. A binder 6/bloodline 2 has an Effective Binder Level of 8, including access to 4th level vestiges because access to those is granted by EBL, but he wouldn't gain the ability to bind a second vestige to him each day because that's a class ability.
-Bloodline levels ARE NOT level adjustments. They are "levels" each character is required to take. Level Adjustment, per Monster Manual page 311, is "a number that is added to the creature's total Hit Dice to arrive at its effective character level."
-Because bloodline levels are not level adjustments, they cannot be bought off.
So you can't buy them off, they are levels, they count for whether a spell can effect you or not, they increase CLASS level calculations as though they were a level in that class, but not for advancing class features or spells known/cast per day.
And, for the third time I address the original issue in this post, they count for whether a spell can effect you or not, they increase CLASS level calculations as though they were a level in that class, but not for advancing class features or spells known/cast per day, and they are a "level" that you take.
Which means they adjust your total character level. It's pretty straight forward and actually simple.
Semi-related:
What, are you casting bloodline levels from a wand now? That rule specifically limits how hit dice are tied to character level, it doesn't link them for all purposes. Try looking up character level. That makes your next argument pointless, and I'm not gonna repeat the line from the bloodline rules 800 times if you won't bother to understand it. I really don't care if you see it differently than I do, I'm never gonna play a game with you. The proof is the statement in question, which you won't accept.
What the fuck idiocy is this entire paragraph? How did anything TML post equate to "casting bloodline levels from wands"? What the fuck, dude? In case you missed it, I posted - in its entirety - the definition of Character Level at the top of my post, and it does nothing but prove you horrifyingly wrong on that entire paragraph.
The only way it doesn't is if you didn't clearly articulate what you meant, and what everyone else is taking it all to mean is not what you actually mean. I would welcome you to rephrase it if that is the case, because arguing against something that isn't what's actually being meant doesn't resolve the issue.
Oh, also, Bloodline levels are not levels in a Prestige Class. Those have a specific definition, too, and call themselves out as PrCs. Bloodlines do not include themselves in this category, so your argument that you can only have 3 levels maximum because it's "just like a PRC" is irrelevant. Kind of like arguing that if I have 3 oranges (prc), I can only have 3 apples (bloodline), because an apple is a fruit (class level), and they both are sold in similar looking baskets at the store.
tl;dr
The bloodlines entry specifically calls them "class levels of bloodline", so any argument they aren't class levels is bullshit and the person is deluding themselves. I just felt like making a wall-of-text post to feel poncy this morning.
Semi-related: I'm not going to start debating the validity of taking more Class Levels of bloodline than the minimum required, since that falls into two categories: 1) it never says how many levels of each bloodline there are, just how many you MUST have at certain points, and 2) It's a "It doesn't specifically say I can't, so I probably can" argument, though it is a valid point.